“…The usual $O(2,2)$ and $S$-duality transformations are just special cases of the string Geroch group, which is infinitesimally identified with the $O(2,2)$ current algebra. …”
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“…A translation of ""On Seeing the Stars"", Nicole Oresme's 14th-century treatise on atmospheric refraction, in which Oresme uses optics and infinitesimals to help solve the problem of astronomy, while proposing that light travels along a curve through the atmosphere.…”
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“…We conclude that rather than life having explored only an infinitesimally small part of sequence space in the last 4 Gyr, it is instead quite plausible for all of functional protein sequence space to have been explored and that furthermore, at the molecular level, there is no role for contingency.…”
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“…This paper will discuss the differences between physical time and experiential time and explain how an expanded system of real analysis containing infinitesimals can resolve the paradoxes of continuity without sacrificing the modern edifice of mathematical physics.…”
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“…We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. …”
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“…The previous work has implicitly assumed that the disease is initialized by an infinitesimally small proportion of the population. Our modifications allow us to account for an arbitrarily large initial proportion infected. …”
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“…Such arrangement is accompanied by a very significant reduction of the source temperature, in principle, to infinitesimally above the ambient temperature and forms the basis for the design of a perfect thermal diffuser with maximal heat dissipation. …”
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“…Plant resistance to this pathogen is highly complex, typically involving numerous polymorphisms with infinitesimally small effects, which makes resistance breeding a major challenge. …”
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“…Moreover, we demonstrate that when the system is at the exceptional point, any infinitesimally small change in the system parameters increases the mode amplitudes. …”
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“…If we split matter down into smaller and infinitesimally smaller pieces, where do we arrive? At the Particle Zoo - the extraordinary subatomic world of antimatter, neutrinos, strange-flavoured quarks and yetis, gravitons, ghosts and glueballs, mindboggling eleven-dimensional strings and the elusive Higgs boson itself. …”
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“…We consider a class of models with gauged U(1)_R symmetry in 4D N=1 supergravity that have, at the classical level, a metastable ground state, an infinitesimally small (tunable) positive cosmological constant and a TeV gravitino mass. …”
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“…The lacking of these results is also connected to the fact that [Formula: see text] is necessarily not a complete ordered set, e.g. the set of all the infinitesimals has neither supremum nor infimum. We present a solution of these problems with the introduction of the notions of hypernatural number, hypersequence, close supremum and infimum. …”
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“…Thefindings of this work were compared to the exact results found previously and were found to be within an infinitesimally negligible margin of error.…”
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“…Examples of the main topics covered include notions of Sobolev space on abstract metric measure spaces; normed modules, which constitute a convenient technical tool for the introduction of a robust differential structure in the nonsmooth setting; first-order differential operators and the corresponding functional spaces; the theory of heat flow and its regularizing properties, within the general framework of “infinitesimally Hilbertian” metric measure spaces; the RCD condition and its effects on the behavior of heat flow; and second-order calculus on RCD spaces. …”
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“…An introduction to the world of quarks and leptons, and of their interactions governed by fundamental symmetries of nature, as well as an introduction to the connection that exists between worlds of the infinitesimally small and the infinitely large. The book starts with a simple presentation of the theoretical framework, the so-called Standard Model, which evolved gradually since the 1960's. …”
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“…This hybrid model is based on treating the membrane permeability and the step change in diffusion coefficient as two interactions separated by an infinitesimally small layer. By conducting an extensive analytical flux analysis, the performance of our hybrid model is compared with a commonly used membrane transit model (reference model). …”
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“…However, that model only applies in the regime of infinitesimally small surface roughness, and consequently it does not capture the decrease in energy loss with surface roughness at the large roughness regime. …”
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“…Furthermore, a threshold condition only depending on such potentials is determined distinguishing the wetting regime, where discrete minimizers are explicitly characterized as configurations contained in an infinitesimally thick layer, i.e., the wetting layer, on the substrate, from the dewetting regime. …”
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“…What are indivisibles and infinitesimals? What are real numbers, continuity, the continuum, differentials, and integrals? …”
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“…Semiochemicals are often produced in infinitesimally small quantities, so their isolation requires large amounts of starting material, not only requiring significant effort in sample preparation, but also resulting in a complex mixture of compounds from which the bioactive compound needs to be purified and identified. …”
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